#### JJBladester

Gold Member

- 286

- 2

**1. The problem statement, all variables and given/known data**

A 20-kg package is at rest on an incline when a force

**P**is applied to it.

__Determine the magnitude of__The static and kinetic coefficients of friction between the package and the incline are both equal to 0.3.

**P**if 10s is required for the package to travel 5m up the incline.*Answer: 419N to start and 301 during sliding*

**2. Relevant equations**

m=20kg

g=9.8m/s

^{2}

t=10s

x

_{i}= 0ft

x

_{f}= 5ft

μ

_{s}= μ

_{k}= 0.3

Frictional force = F

_{f}= μN

**3. The attempt at a solution**

First, I drew a free-body diagram including tilted coordinate axes:

Then, I went about finding the sum of the forces equations in the x- and y-directions.

[tex]\sum F_{x}=-F_{f}-mgsin(20)+Pcos(30)=ma[/tex]

[tex]\sum F_{y}=N-mgcos(20)-Psin(30)=0[/tex]

From the second equation,

[tex]N=mgcos(20)+Psin(30)[/tex]

Plugging this value for N into F

_{f}= μN in the first equation yields:

[tex]P=\frac{m\left(a+\mu gcos(20)+gsin(20)\right)}{cos(30)-\mu sin(30)}[/tex]

If I know the acceleration, I can find the magnitude of

**P**. There has to be a way to find acceleration from the initial conditions, but I'm at a loss. Also, once static friction is overcome, I'm sure the

*sum of the forces*equations will be different but I'm not sure how.